The theory, which I don’t find entirely convincing, is that African, and to a lesser extent Asian, megafauna were around when humans evolved and had time to learn to adapt to them.
In the Americas, Oz and elsewhere the animals weren’t adapted to this uniquely effective predator and were wiped out by us.
Just curious, but how much have you actually looked into the distribution of massive accumulations of megafauna remains and other detritus deposited at or near the end of the last glaciation in North America and elsewhere?
In any case, for me, the "hunted to extinction" narrative has a "man made global warming" ring to it.